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تسجيل مستخدم جديدUndulated Bilayer Interfaces in the Planar Functionalized Cahn-Hilliard Equation
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Experiments with diblock co-polymer melts display undulated bilayers that emanate from defects such as triple junctions and endcaps, cite{batesjain_2004}. Undulated bilayers are characterized by oscillatory perturbations of the bilayer width, which decay on a spatial length scale that is long compared to the bilayer width. We mimic defects within the functionalized Cahn-Hillard free energy by introducing spatially localized inhomogeneities within its parameters. For length parameter $varepsilonll1$, we show that this induces undulated bilayer solutions whose width perturbations decay on an $O!left(varepsilon^{-1/2}right)$ inner length scale that is long in comparison to the $O(1)$ scale that characterizes the bilayer width.
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